5(8n-1)(3n-7)=0

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Solution for 5(8n-1)(3n-7)=0 equation: 


Simplifying
5(8n + -1)(3n + -7) = 0

Reorder the terms:
5(-1 + 8n)(3n + -7) = 0

Reorder the terms:
5(-1 + 8n)(-7 + 3n) = 0

Multiply (-1 + 8n) * (-7 + 3n)
5(-1(-7 + 3n) + 8n * (-7 + 3n)) = 0
5((-7 * -1 + 3n * -1) + 8n * (-7 + 3n)) = 0
5((7 + -3n) + 8n * (-7 + 3n)) = 0
5(7 + -3n + (-7 * 8n + 3n * 8n)) = 0
5(7 + -3n + (-56n + 24n2)) = 0

Combine like terms: -3n + -56n = -59n
5(7 + -59n + 24n2) = 0
(7 * 5 + -59n * 5 + 24n2 * 5) = 0
(35 + -295n + 120n2) = 0

Solving
35 + -295n + 120n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '5'.
5(7 + -59n + 24n2) = 0

Factor a trinomial.
5((1 + -8n)(7 + -3n)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(1 + -8n)' equal to zero and attempt to solve:

Simplifying
1 + -8n = 0

Solving
1 + -8n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -8n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8n = 0 + -1
-8n = 0 + -1

Combine like terms: 0 + -1 = -1
-8n = -1

Divide each side by '-8'.
n = 0.125

Simplifying
n = 0.125

Subproblem 2
Set the factor '(7 + -3n)' equal to zero and attempt to solve:

Simplifying
7 + -3n = 0

Solving
7 + -3n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -3n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3n = 0 + -7
-3n = 0 + -7

Combine like terms: 0 + -7 = -7
-3n = -7

Divide each side by '-3'.
n = 2.333333333

Simplifying
n = 2.333333333
Solution
n = {0.125, 2.333333333}

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